TSTP Solution File: SWW640_2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWW640_2 : TPTP v8.1.0. Released v6.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 29 20:59:31 EDT 2022
% Result : Theorem 0.20s 0.47s
% Output : Proof 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.12 % Problem : SWW640_2 : TPTP v8.1.0. Released v6.1.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Sun Sep 4 20:41:16 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.20/0.47 % SZS status Theorem
% 0.20/0.47 % SZS output start Proof
% 0.20/0.47 tff(tb2t_type, type, (
% 0.20/0.47 tb2t: uni > $int)).
% 0.20/0.47 tff(t2tb_type, type, (
% 0.20/0.47 t2tb: $int > uni)).
% 0.20/0.47 tff(str_proj_31_type, type, (
% 0.20/0.47 str_proj_31: rope1 > $int)).
% 0.20/0.47 tff(tptp_fun_X1_8_type, type, (
% 0.20/0.47 tptp_fun_X1_8: rope1)).
% 0.20/0.47 tff(match_rope1_type, type, (
% 0.20/0.47 match_rope1: ( ty * rope1 * uni * uni * uni ) > uni)).
% 0.20/0.47 tff(app_proj_31_type, type, (
% 0.20/0.47 app_proj_31: rope1 > $int)).
% 0.20/0.47 tff(int_type, type, (
% 0.20/0.47 int: ty)).
% 0.20/0.47 tff(str1_type, type, (
% 0.20/0.47 str1: ( string2 * $int * $int ) > rope1)).
% 0.20/0.47 tff(str_proj_21_type, type, (
% 0.20/0.47 str_proj_21: rope1 > $int)).
% 0.20/0.47 tff(str_proj_11_type, type, (
% 0.20/0.47 str_proj_11: rope1 > string2)).
% 0.20/0.47 tff(sort1_type, type, (
% 0.20/0.47 sort1: ( ty * uni ) > $o)).
% 0.20/0.47 tff(app3_type, type, (
% 0.20/0.47 app3: ( rope1 * rope1 * $int ) > rope1)).
% 0.20/0.47 tff(app_proj_21_type, type, (
% 0.20/0.47 app_proj_21: rope1 > rope1)).
% 0.20/0.47 tff(app_proj_11_type, type, (
% 0.20/0.47 app_proj_11: rope1 > rope1)).
% 0.20/0.47 tff(length4_type, type, (
% 0.20/0.47 length4: rope1 > $int)).
% 0.20/0.47 tff(emp1_type, type, (
% 0.20/0.47 emp1: rope1)).
% 0.20/0.47 tff(tptp_fun_X_9_type, type, (
% 0.20/0.47 tptp_fun_X_9: rope1)).
% 0.20/0.47 tff(tptp_fun_X2_7_type, type, (
% 0.20/0.47 tptp_fun_X2_7: $int)).
% 0.20/0.47 tff(inv1_type, type, (
% 0.20/0.47 inv1: rope1 > $o)).
% 0.20/0.47 tff(length3_type, type, (
% 0.20/0.47 length3: string2 > $int)).
% 0.20/0.47 tff(tptp_fun_R_4_type, type, (
% 0.20/0.47 tptp_fun_R_4: rope1)).
% 0.20/0.47 tff(string_of_queue1_type, type, (
% 0.20/0.47 string_of_queue1: array_rope > string2)).
% 0.20/0.47 tff(tb2t1_type, type, (
% 0.20/0.47 tb2t1: uni > array_rope)).
% 0.20/0.47 tff(mk_array1_type, type, (
% 0.20/0.47 mk_array1: ( ty * $int * uni ) > uni)).
% 0.20/0.47 tff(t2tb3_type, type, (
% 0.20/0.47 t2tb3: map_int_rope > uni)).
% 0.20/0.47 tff(tptp_fun_Q1_5_type, type, (
% 0.20/0.47 tptp_fun_Q1_5: map_int_rope)).
% 0.20/0.47 tff(tptp_fun_Q_6_type, type, (
% 0.20/0.47 tptp_fun_Q_6: $int)).
% 0.20/0.47 tff(rope_type, type, (
% 0.20/0.47 rope: ty)).
% 0.20/0.47 tff(fib1_type, type, (
% 0.20/0.47 fib1: $int > $int)).
% 0.20/0.47 tff(max3_type, type, (
% 0.20/0.47 max3: $int)).
% 0.20/0.47 tff(infix_eqeq1_type, type, (
% 0.20/0.47 infix_eqeq1: ( string2 * string2 ) > $o)).
% 0.20/0.47 tff(app2_type, type, (
% 0.20/0.47 app2: ( string2 * string2 ) > string2)).
% 0.20/0.47 tff(string3_type, type, (
% 0.20/0.47 string3: rope1 > string2)).
% 0.20/0.47 tff(tptp_fun_Q2_10_type, type, (
% 0.20/0.47 tptp_fun_Q2_10: map_int_rope)).
% 0.20/0.47 tff(tb2t2_type, type, (
% 0.20/0.47 tb2t2: uni > rope1)).
% 0.20/0.47 tff(get_type, type, (
% 0.20/0.47 get: ( ty * ty * uni * uni ) > uni)).
% 0.20/0.47 tff(mixfix_lbrb1_type, type, (
% 0.20/0.47 mixfix_lbrb1: ( string2 * $int ) > char1)).
% 0.20/0.47 tff(tptp_fun_I_0_type, type, (
% 0.20/0.47 tptp_fun_I_0: ( string2 * string2 ) > $int)).
% 0.20/0.47 tff(1,plain,
% 0.20/0.47 (^[X: $int] : refl(sort1(int, t2tb(X)) <=> sort1(int, t2tb(X)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(2,plain,
% 0.20/0.47 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[1])).
% 0.20/0.47 tff(3,plain,
% 0.20/0.47 (![X: $int] : sort1(int, t2tb(X)) <=> ![X: $int] : sort1(int, t2tb(X))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(4,axiom,(![X: $int] : sort1(int, t2tb(X))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','t2tb_sort')).
% 0.20/0.47 tff(5,plain,
% 0.20/0.47 (![X: $int] : sort1(int, t2tb(X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.20/0.47 tff(6,plain,(
% 0.20/0.47 ![X: $int] : sort1(int, t2tb(X))),
% 0.20/0.47 inference(skolemize,[status(sab)],[5])).
% 0.20/0.47 tff(7,plain,
% 0.20/0.47 (![X: $int] : sort1(int, t2tb(X))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[6, 2])).
% 0.20/0.47 tff(8,plain,
% 0.20/0.47 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(str_proj_31(X1!8)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(9,plain,
% 0.20/0.47 (sort1(int, t2tb(str_proj_31(X1!8)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[8, 7])).
% 0.20/0.47 tff(10,plain,
% 0.20/0.47 (^[A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : refl(((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)) <=> ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(11,plain,
% 0.20/0.47 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[10])).
% 0.20/0.47 tff(12,plain,
% 0.20/0.47 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(13,plain,
% 0.20/0.47 (^[A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : rewrite((sort1(A, Z1) => (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)) <=> ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(14,plain,
% 0.20/0.47 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : (sort1(A, Z1) => (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(quant_intro,[status(thm)],[13])).
% 0.20/0.47 tff(15,axiom,(![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : (sort1(A, Z1) => (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','match_rope_Str1')).
% 0.20/0.47 tff(16,plain,
% 0.20/0.47 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[15, 14])).
% 0.20/0.47 tff(17,plain,
% 0.20/0.47 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[16, 12])).
% 0.20/0.47 tff(18,plain,(
% 0.20/0.47 ![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(skolemize,[status(sab)],[17])).
% 0.20/0.47 tff(19,plain,
% 0.20/0.47 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[18, 11])).
% 0.20/0.47 tff(20,plain,
% 0.20/0.47 (((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))) | ((~sort1(int, t2tb(str_proj_31(X1!8)))) | (match_rope1(int, str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(str_proj_31(X1!8))))) <=> ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))) | (~sort1(int, t2tb(str_proj_31(X1!8)))) | (match_rope1(int, str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(str_proj_31(X1!8))))),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(21,plain,
% 0.20/0.47 ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))) | ((~sort1(int, t2tb(str_proj_31(X1!8)))) | (match_rope1(int, str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(str_proj_31(X1!8))))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(22,plain,
% 0.20/0.47 ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: string2, U1: $int, U2: $int] : ((~sort1(A, Z1)) | (match_rope1(A, str1(U, U1, U2), Z, Z1, Z2) = Z1))) | (~sort1(int, t2tb(str_proj_31(X1!8)))) | (match_rope1(int, str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(str_proj_31(X1!8)))),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[21, 20])).
% 0.20/0.47 tff(23,plain,
% 0.20/0.47 (match_rope1(int, str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(str_proj_31(X1!8))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[22, 19, 9])).
% 0.20/0.47 tff(24,plain,
% 0.20/0.47 (^[I: $int] : refl(($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(25,plain,
% 0.20/0.47 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[24])).
% 0.20/0.47 tff(26,plain,
% 0.20/0.47 (^[I: $int] : trans(monotonicity(rewrite($sum(tb2t(t2tb(I)), $product(-1, I)) = $sum($product(-1, I), tb2t(t2tb(I)))), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum($product(-1, I), tb2t(t2tb(I))) = 0))), rewrite(($sum($product(-1, I), tb2t(t2tb(I))) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)), (($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(27,plain,
% 0.20/0.47 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0) <=> ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[26])).
% 0.20/0.47 tff(28,plain,
% 0.20/0.47 (^[I: $int] : rewrite((tb2t(t2tb(I)) = I) <=> ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0))),
% 0.20/0.47 inference(bind,[status(th)],[])).
% 0.20/0.47 tff(29,plain,
% 0.20/0.47 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.20/0.47 inference(quant_intro,[status(thm)],[28])).
% 0.20/0.47 tff(30,plain,
% 0.20/0.47 (![I: $int] : (tb2t(t2tb(I)) = I) <=> ![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.20/0.47 inference(rewrite,[status(thm)],[])).
% 0.20/0.47 tff(31,axiom,(![I: $int] : (tb2t(t2tb(I)) = I)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','bridgeL')).
% 0.20/0.47 tff(32,plain,
% 0.20/0.47 (![I: $int] : (tb2t(t2tb(I)) = I)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[31, 30])).
% 0.20/0.47 tff(33,plain,
% 0.20/0.47 (![I: $int] : ($sum(tb2t(t2tb(I)), $product(-1, I)) = 0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[32, 29])).
% 0.20/0.47 tff(34,plain,
% 0.20/0.47 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[33, 27])).
% 0.20/0.47 tff(35,plain,(
% 0.20/0.47 ![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.47 inference(skolemize,[status(sab)],[34])).
% 0.20/0.47 tff(36,plain,
% 0.20/0.47 (![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)),
% 0.20/0.47 inference(modus_ponens,[status(thm)],[35, 25])).
% 0.20/0.47 tff(37,plain,
% 0.20/0.47 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))) = 0)),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(38,plain,
% 0.20/0.47 ($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))) = 0),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[37, 36])).
% 0.20/0.47 tff(39,plain,
% 0.20/0.47 ((~($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))) = 0)) | $lesseq($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(40,plain,
% 0.20/0.47 ($lesseq($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[39, 38])).
% 0.20/0.47 tff(41,plain,
% 0.20/0.47 ((~($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))) = 0)) | $greatereq($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))), 0)),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.47 tff(42,plain,
% 0.20/0.47 ($greatereq($sum(str_proj_31(X1!8), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))), 0)),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[41, 38])).
% 0.20/0.47 tff(43,plain,
% 0.20/0.47 (str_proj_31(X1!8) = tb2t(t2tb(str_proj_31(X1!8)))),
% 0.20/0.47 inference(theory_lemma,[status(thm)],[42, 40])).
% 0.20/0.47 tff(44,plain,
% 0.20/0.47 (tb2t(t2tb(str_proj_31(X1!8))) = str_proj_31(X1!8)),
% 0.20/0.47 inference(symmetry,[status(thm)],[43])).
% 0.20/0.47 tff(45,plain,
% 0.20/0.47 (str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))) = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))),
% 0.20/0.47 inference(monotonicity,[status(thm)],[44])).
% 0.20/0.47 tff(46,plain,
% 0.20/0.47 (str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8)) = str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))),
% 0.20/0.47 inference(symmetry,[status(thm)],[45])).
% 0.20/0.47 tff(47,plain,
% 0.20/0.47 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(app_proj_31(X1!8)))),
% 0.20/0.47 inference(quant_inst,[status(thm)],[])).
% 0.20/0.47 tff(48,plain,
% 0.20/0.47 (sort1(int, t2tb(app_proj_31(X1!8)))),
% 0.20/0.47 inference(unit_resolution,[status(thm)],[47, 7])).
% 0.20/0.47 tff(49,plain,
% 0.20/0.47 (^[A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : refl(((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)) <=> ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(50,plain,
% 0.20/0.48 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[49])).
% 0.20/0.48 tff(51,plain,
% 0.20/0.48 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(52,plain,
% 0.20/0.48 (^[A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : rewrite((sort1(A, Z2) => (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)) <=> ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(53,plain,
% 0.20/0.48 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : (sort1(A, Z2) => (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[52])).
% 0.20/0.48 tff(54,axiom,(![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : (sort1(A, Z2) => (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','match_rope_App1')).
% 0.20/0.48 tff(55,plain,
% 0.20/0.48 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[54, 53])).
% 0.20/0.48 tff(56,plain,
% 0.20/0.48 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[55, 51])).
% 0.20/0.48 tff(57,plain,(
% 0.20/0.48 ![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(skolemize,[status(sab)],[56])).
% 0.20/0.48 tff(58,plain,
% 0.20/0.48 (![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[57, 50])).
% 0.20/0.48 tff(59,plain,
% 0.20/0.48 (((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | ((~sort1(int, t2tb(app_proj_31(X1!8)))) | (match_rope1(int, app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(app_proj_31(X1!8))))) <=> ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | (~sort1(int, t2tb(app_proj_31(X1!8)))) | (match_rope1(int, app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(app_proj_31(X1!8))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(60,plain,
% 0.20/0.48 ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | ((~sort1(int, t2tb(app_proj_31(X1!8)))) | (match_rope1(int, app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(app_proj_31(X1!8))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(61,plain,
% 0.20/0.48 ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | (~sort1(int, t2tb(app_proj_31(X1!8)))) | (match_rope1(int, app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(app_proj_31(X1!8)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[60, 59])).
% 0.20/0.48 tff(62,plain,
% 0.20/0.48 (match_rope1(int, app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(app_proj_31(X1!8))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[61, 58, 48])).
% 0.20/0.48 tff(63,plain,
% 0.20/0.48 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))) = 0)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(64,plain,
% 0.20/0.48 ($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))) = 0),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[63, 36])).
% 0.20/0.48 tff(65,plain,
% 0.20/0.48 ((~($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))) = 0)) | $lesseq($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))), 0)),
% 0.20/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.48 tff(66,plain,
% 0.20/0.48 ($lesseq($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))), 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[65, 64])).
% 0.20/0.48 tff(67,plain,
% 0.20/0.48 ((~($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))) = 0)) | $greatereq($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))), 0)),
% 0.20/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.48 tff(68,plain,
% 0.20/0.48 ($greatereq($sum(app_proj_31(X1!8), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))), 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[67, 64])).
% 0.20/0.48 tff(69,plain,
% 0.20/0.48 (app_proj_31(X1!8) = tb2t(t2tb(app_proj_31(X1!8)))),
% 0.20/0.48 inference(theory_lemma,[status(thm)],[68, 66])).
% 0.20/0.48 tff(70,plain,
% 0.20/0.48 (tb2t(t2tb(app_proj_31(X1!8))) = app_proj_31(X1!8)),
% 0.20/0.48 inference(symmetry,[status(thm)],[69])).
% 0.20/0.48 tff(71,plain,
% 0.20/0.48 (app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))) = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[70])).
% 0.20/0.48 tff(72,plain,
% 0.20/0.48 (app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8)) = app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))),
% 0.20/0.48 inference(symmetry,[status(thm)],[71])).
% 0.20/0.48 tff(73,assumption,(X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))), introduced(assumption)).
% 0.20/0.48 tff(74,plain,
% 0.20/0.48 (X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))),
% 0.20/0.48 inference(transitivity,[status(thm)],[73, 72])).
% 0.20/0.48 tff(75,plain,
% 0.20/0.48 (match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = match_rope1(int, app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[74])).
% 0.20/0.48 tff(76,plain,
% 0.20/0.48 (match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(app_proj_31(X1!8))),
% 0.20/0.48 inference(transitivity,[status(thm)],[75, 62])).
% 0.20/0.48 tff(77,plain,
% 0.20/0.48 (tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = tb2t(t2tb(app_proj_31(X1!8)))),
% 0.20/0.48 inference(monotonicity,[status(thm)],[76])).
% 0.20/0.48 tff(78,plain,
% 0.20/0.48 ((~(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = tb2t(t2tb(app_proj_31(X1!8))))) | $lesseq($sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))), 0)),
% 0.20/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.48 tff(79,plain,
% 0.20/0.48 ($lesseq($sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, tb2t(t2tb(app_proj_31(X1!8))))), 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[78, 77])).
% 0.20/0.48 tff(80,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : refl(($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0) <=> ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(81,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0) <=> ![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[80])).
% 0.20/0.48 tff(82,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : trans(monotonicity(rewrite($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = $sum($product(-1, X2), length4(app3(X, X1, X2)))), (($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = 0) <=> ($sum($product(-1, X2), length4(app3(X, X1, X2))) = 0))), rewrite(($sum($product(-1, X2), length4(app3(X, X1, X2))) = 0) <=> ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)), (($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = 0) <=> ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(83,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : ($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = 0) <=> ![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[82])).
% 0.20/0.48 tff(84,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : rewrite((length4(app3(X, X1, X2)) = X2) <=> ($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = 0))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(85,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (length4(app3(X, X1, X2)) = X2) <=> ![X: rope1, X1: rope1, X2: $int] : ($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = 0)),
% 0.20/0.48 inference(quant_intro,[status(thm)],[84])).
% 0.20/0.48 tff(86,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (length4(app3(X, X1, X2)) = X2) <=> ![X: rope1, X1: rope1, X2: $int] : (length4(app3(X, X1, X2)) = X2)),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(87,axiom,(((length4(emp1) = 0) & ![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2)) & ![X: rope1, X1: rope1, X2: $int] : (length4(app3(X, X1, X2)) = X2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','length_def')).
% 0.20/0.48 tff(88,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (length4(app3(X, X1, X2)) = X2)),
% 0.20/0.48 inference(and_elim,[status(thm)],[87])).
% 0.20/0.48 tff(89,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (length4(app3(X, X1, X2)) = X2)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[88, 86])).
% 0.20/0.48 tff(90,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : ($sum(length4(app3(X, X1, X2)), $product(-1, X2)) = 0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[89, 85])).
% 0.20/0.48 tff(91,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[90, 83])).
% 0.20/0.48 tff(92,plain,(
% 0.20/0.48 ![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)),
% 0.20/0.48 inference(skolemize,[status(sab)],[91])).
% 0.20/0.48 tff(93,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[92, 81])).
% 0.20/0.48 tff(94,plain,
% 0.20/0.48 ((~![X: rope1, X1: rope1, X2: $int] : ($sum(X2, $product(-1, length4(app3(X, X1, X2)))) = 0)) | ($sum(tb2t(t2tb(app_proj_31(X1!8))), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))) = 0)),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(95,plain,
% 0.20/0.48 ($sum(tb2t(t2tb(app_proj_31(X1!8))), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))) = 0),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[94, 93])).
% 0.20/0.48 tff(96,plain,
% 0.20/0.48 ((~($sum(tb2t(t2tb(app_proj_31(X1!8))), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))) = 0)) | $lesseq($sum(tb2t(t2tb(app_proj_31(X1!8))), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))), 0)),
% 0.20/0.48 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.48 tff(97,plain,
% 0.20/0.48 ($lesseq($sum(tb2t(t2tb(app_proj_31(X1!8))), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))), 0)),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[96, 95])).
% 0.20/0.48 tff(98,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : refl((inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))))) <=> (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(99,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))))) <=> ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[98])).
% 0.20/0.48 tff(100,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : rewrite((inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))) <=> (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(101,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))) <=> ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[100])).
% 0.20/0.48 tff(102,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : rewrite((inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X)), $product(-1, length4(X1)))) = 0))) <=> (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(103,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X)), $product(-1, length4(X1)))) = 0))) <=> ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[102])).
% 0.20/0.48 tff(104,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : rewrite((inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1))))) <=> (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X)), $product(-1, length4(X1)))) = 0))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(105,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1))))) <=> ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X)), $product(-1, length4(X1)))) = 0)))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[104])).
% 0.20/0.48 tff(106,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1))))) <=> ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1)))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(107,plain,
% 0.20/0.48 (^[X: rope1, X1: rope1, X2: $int] : rewrite((inv1(app3(X, X1, X2)) <=> (((($less(0, length4(X)) & inv1(X)) & $less(0, length4(X1))) & inv1(X1)) & (X2 = $sum(length4(X), length4(X1))))) <=> (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1))))))),
% 0.20/0.48 inference(bind,[status(th)],[])).
% 0.20/0.48 tff(108,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (((($less(0, length4(X)) & inv1(X)) & $less(0, length4(X1))) & inv1(X1)) & (X2 = $sum(length4(X), length4(X1))))) <=> ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1)))))),
% 0.20/0.48 inference(quant_intro,[status(thm)],[107])).
% 0.20/0.48 tff(109,axiom,((inv1(emp1) & ![X: string2, X1: $int, X2: $int] : (inv1(str1(X, X1, X2)) <=> ((($less(0, X2) & $lesseq(0, X1)) & $less(X1, length3(X))) & $lesseq($sum(X1, X2), length3(X))))) & ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (((($less(0, length4(X)) & inv1(X)) & $less(0, length4(X1))) & inv1(X1)) & (X2 = $sum(length4(X), length4(X1)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','inv_def')).
% 0.20/0.48 tff(110,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (((($less(0, length4(X)) & inv1(X)) & $less(0, length4(X1))) & inv1(X1)) & (X2 = $sum(length4(X), length4(X1)))))),
% 0.20/0.48 inference(and_elim,[status(thm)],[109])).
% 0.20/0.48 tff(111,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[110, 108])).
% 0.20/0.48 tff(112,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & (X2 = $sum(length4(X), length4(X1)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[111, 106])).
% 0.20/0.48 tff(113,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X)), $product(-1, length4(X1)))) = 0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[112, 105])).
% 0.20/0.48 tff(114,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[113, 103])).
% 0.20/0.48 tff(115,plain,(
% 0.20/0.48 ![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> ((~$lesseq(length4(X), 0)) & inv1(X) & (~$lesseq(length4(X1), 0)) & inv1(X1) & ($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))),
% 0.20/0.48 inference(skolemize,[status(sab)],[114])).
% 0.20/0.48 tff(116,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[115, 101])).
% 0.20/0.48 tff(117,plain,
% 0.20/0.48 (![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))))),
% 0.20/0.48 inference(modus_ponens,[status(thm)],[116, 99])).
% 0.20/0.48 tff(118,plain,
% 0.20/0.48 ((~![X: rope1, X1: rope1, X2: $int] : (inv1(app3(X, X1, X2)) <=> (~($lesseq(length4(X1), 0) | $lesseq(length4(X), 0) | (~inv1(X)) | (~inv1(X1)) | (~($sum(X2, $sum($product(-1, length4(X1)), $product(-1, length4(X)))) = 0)))))) | (inv1(app3(X!9, X1!8, X2!7)) <=> (~($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0)))))),
% 0.20/0.48 inference(quant_inst,[status(thm)],[])).
% 0.20/0.48 tff(119,plain,
% 0.20/0.48 (inv1(app3(X!9, X1!8, X2!7)) <=> (~($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0))))),
% 0.20/0.48 inference(unit_resolution,[status(thm)],[118, 117])).
% 0.20/0.48 tff(120,plain,
% 0.20/0.48 ((($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0))) & ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7)))) <=> ($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0)) & $lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & inv1(X!9) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(121,plain,
% 0.20/0.48 ((($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) & ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0))) & (R!4 = app3(X!9, X1!8, X2!7))) <=> ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(122,plain,
% 0.20/0.48 ((~(~(R!4 = app3(X!9, X1!8, X2!7)))) <=> (R!4 = app3(X!9, X1!8, X2!7))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(123,plain,
% 0.20/0.48 (((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) <=> ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(124,plain,
% 0.20/0.48 (($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) <=> ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(125,plain,
% 0.20/0.48 (($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) <=> ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))),
% 0.20/0.48 inference(rewrite,[status(thm)],[])).
% 0.20/0.48 tff(126,plain,
% 0.20/0.48 ((~(~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0))) <=> $lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0)),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(127,plain,
% 0.20/0.49 ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0)) <=> (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(128,plain,
% 0.20/0.49 ((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) <=> (~(~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[127])).
% 0.20/0.49 tff(129,plain,
% 0.20/0.49 ((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) <=> $lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0)),
% 0.20/0.49 inference(transitivity,[status(thm)],[128, 126])).
% 0.20/0.49 tff(130,plain,
% 0.20/0.49 (((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) <=> ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[129, 125])).
% 0.20/0.49 tff(131,plain,
% 0.20/0.49 (((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) <=> ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))),
% 0.20/0.49 inference(transitivity,[status(thm)],[130, 124])).
% 0.20/0.49 tff(132,plain,
% 0.20/0.49 ((((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) & ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) & (~(~(R!4 = app3(X!9, X1!8, X2!7))))) <=> (($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) & ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0))) & (R!4 = app3(X!9, X1!8, X2!7)))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[131, 123, 122])).
% 0.20/0.49 tff(133,plain,
% 0.20/0.49 ((((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) & ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) & (~(~(R!4 = app3(X!9, X1!8, X2!7))))) <=> ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[132, 121])).
% 0.20/0.49 tff(134,plain,
% 0.20/0.49 (($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(Q!6, $product(-1, max3)) = 1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) <=> ($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0)))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(135,plain,
% 0.20/0.49 ((($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(Q!6, $product(-1, max3)) = 1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) & (((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) & ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) & (~(~(R!4 = app3(X!9, X1!8, X2!7)))))) <=> (($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0))) & ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & $greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7))))),
% 0.20/0.49 inference(monotonicity,[status(thm)],[134, 133])).
% 0.20/0.49 tff(136,plain,
% 0.20/0.49 ((($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(Q!6, $product(-1, max3)) = 1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) & (((~(~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, fib1($sum(1, max3))))), 0))) & ($greatereq(Q!6, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) & ((~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(X!9) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $product(-1, fib1($sum(1, max3))))), 0))) & (~(~(R!4 = app3(X!9, X1!8, X2!7)))))) <=> ($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0)) & $lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & inv1(X!9) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7)))),
% 0.20/0.49 inference(transitivity,[status(thm)],[135, 120])).
% 0.20/0.49 tff(137,plain,
% 0.20/0.49 ((~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : (![Q2: map_int_rope] : ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), $sum(tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1)))), $product(-1, fib1($sum(1, max3))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(max3, $product(-1, Q)) = -1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | (~(R = app3(X, X1, X2)))))) <=> (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : (![Q2: map_int_rope] : ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), $sum(tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1)))), $product(-1, fib1($sum(1, max3))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(max3, $product(-1, Q)) = -1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | (~(R = app3(X, X1, X2))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(138,plain,
% 0.20/0.49 ((~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))))), $product(-1, tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))))), $product(-1, tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))))), $product(-1, tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))))), 0))))))) <=> (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : (![Q2: map_int_rope] : ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), $sum(tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1)))), $product(-1, fib1($sum(1, max3))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(max3, $product(-1, Q)) = -1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | (~(R = app3(X, X1, X2))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(139,plain,
% 0.20/0.49 ((~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))) <=> (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))))), $product(-1, tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))))), $product(-1, tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))))), $product(-1, tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))))), 0)))))))),
% 0.20/0.49 inference(rewrite,[status(thm)],[])).
% 0.20/0.49 tff(140,plain,
% 0.20/0.49 ((~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))) <=> (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(141,plain,
% 0.20/0.50 ((~![Q: $int, Q1: map_int_rope, R: rope1] : (((((($lesseq(0, Q) & $less(2, Q)) & (Q = $sum(max3, 1))) & inv1(R)) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))))) & $less($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))), fib1($sum(max3, 1)))) => ![X: rope1, X1: rope1, X2: $int] : ((R = app3(X, X1, X2)) => ((((($less(2, Q) & (Q = $sum(max3, 1))) & inv1(X)) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))))) & $less($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))), fib1($sum(max3, 1)))) => ![Q2: map_int_rope] : ((($lesseq(0, Q) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))) => $less($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))), fib1($sum(max3, 1)))))))) <=> (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))))))))))),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(142,axiom,(~![Q: $int, Q1: map_int_rope, R: rope1] : (((((($lesseq(0, Q) & $less(2, Q)) & (Q = $sum(max3, 1))) & inv1(R)) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))))) & $less($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))), fib1($sum(max3, 1)))) => ![X: rope1, X1: rope1, X2: $int] : ((R = app3(X, X1, X2)) => ((((($less(2, Q) & (Q = $sum(max3, 1))) & inv1(X)) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))))) & $less($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))), fib1($sum(max3, 1)))) => ![Q2: map_int_rope] : ((($lesseq(0, Q) & ![J: $int] : (($lesseq(2, J) & $lesseq(J, max3)) => inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))) => $less($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))), fib1($sum(max3, 1)))))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','wP_parameter_insert_leaves')).
% 0.20/0.50 tff(143,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[142, 141])).
% 0.20/0.50 tff(144,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[143, 140])).
% 0.20/0.50 tff(145,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[144, 140])).
% 0.20/0.50 tff(146,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[145, 140])).
% 0.20/0.50 tff(147,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($lesseq(0, Q) & (~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(R) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))) | (~($lesseq(0, Q) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J))))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & (Q = $sum(1, max3)) & inv1(X) & ![J: $int] : ((~($lesseq(2, J) & $lesseq(J, max3))) | inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J))))) & (~$lesseq(fib1($sum(1, max3)), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))))))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[146, 140])).
% 0.20/0.50 tff(148,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))))), $product(-1, tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R))))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : ((~(R = app3(X, X1, X2))) | ![Q2: map_int_rope] : ((~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))))), $product(-1, tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1))))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))))), $product(-1, tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X))))))), 0))))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[147, 139])).
% 0.20/0.50 tff(149,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : (![Q2: map_int_rope] : ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), $sum(tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1)))), $product(-1, fib1($sum(1, max3))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(max3, $product(-1, Q)) = -1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | (~(R = app3(X, X1, X2)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[148, 138])).
% 0.20/0.50 tff(150,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : (![Q2: map_int_rope] : ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), $sum(tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1)))), $product(-1, fib1($sum(1, max3))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(max3, $product(-1, Q)) = -1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | (~(R = app3(X, X1, X2)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[149, 137])).
% 0.20/0.50 tff(151,plain,
% 0.20/0.50 (~![Q: $int, Q1: map_int_rope, R: rope1] : ((~($greatereq(Q, 0) & (~$lesseq(Q, 2)) & ($sum(Q, $product(-1, max3)) = 1) & inv1(R) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, R, t2tb(0), t2tb(str_proj_31(R)), t2tb(app_proj_31(R)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | ![X: rope1, X1: rope1, X2: $int] : (![Q2: map_int_rope] : ((~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2))))), $sum(tb2t(match_rope1(int, X1, t2tb(0), t2tb(str_proj_31(X1)), t2tb(app_proj_31(X1)))), $product(-1, fib1($sum(1, max3))))), 0)) | (~($greatereq(Q, 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q2)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1)))), string3(X)))))) | (~((~$lesseq(Q, 2)) & ($sum(max3, $product(-1, Q)) = -1) & inv1(X) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$greatereq($sum(tb2t(match_rope1(int, X, t2tb(0), t2tb(str_proj_31(X)), t2tb(app_proj_31(X)))), $sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q, t2tb3(Q1))))), $product(-1, fib1($sum(1, max3))))), 0)))) | (~(R = app3(X, X1, X2)))))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[150, 137])).
% 0.20/0.50 tff(152,plain,
% 0.20/0.50 ($greatereq(Q!6, 0) & (~$lesseq(Q!6, 2)) & ($sum(max3, $product(-1, Q!6)) = -1) & inv1(R!4) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q1!5), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0)) & $lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0) & ![J: $int] : (inv1(tb2t2(get(rope, int, t2tb3(Q2!10), t2tb(J)))) | (~($greatereq(J, 2) & $lesseq($sum(J, $product(-1, max3)), 0)))) & infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) & inv1(X!9) & (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))), $product(-1, tb2t(match_rope1(int, X!9, t2tb(0), t2tb(str_proj_31(X!9)), t2tb(app_proj_31(X!9))))))), 0)) & (R!4 = app3(X!9, X1!8, X2!7))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[151, 136])).
% 0.20/0.50 tff(153,plain,
% 0.20/0.50 (R!4 = app3(X!9, X1!8, X2!7)),
% 0.20/0.50 inference(and_elim,[status(thm)],[152])).
% 0.20/0.50 tff(154,plain,
% 0.20/0.50 (app3(X!9, X1!8, X2!7) = R!4),
% 0.20/0.50 inference(symmetry,[status(thm)],[153])).
% 0.20/0.50 tff(155,plain,
% 0.20/0.50 (inv1(app3(X!9, X1!8, X2!7)) <=> inv1(R!4)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.50 tff(156,plain,
% 0.20/0.50 (inv1(R!4) <=> inv1(app3(X!9, X1!8, X2!7))),
% 0.20/0.50 inference(symmetry,[status(thm)],[155])).
% 0.20/0.50 tff(157,plain,
% 0.20/0.50 (inv1(R!4)),
% 0.20/0.50 inference(and_elim,[status(thm)],[152])).
% 0.20/0.50 tff(158,plain,
% 0.20/0.50 (inv1(app3(X!9, X1!8, X2!7))),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[157, 156])).
% 0.20/0.50 tff(159,plain,
% 0.20/0.50 ((~(inv1(app3(X!9, X1!8, X2!7)) <=> (~($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0)))))) | (~inv1(app3(X!9, X1!8, X2!7))) | (~($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0))))),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(160,plain,
% 0.20/0.50 (~($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0)))),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[159, 158, 119])).
% 0.20/0.50 tff(161,plain,
% 0.20/0.50 (($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0))) | ($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0)),
% 0.20/0.50 inference(tautology,[status(thm)],[])).
% 0.20/0.50 tff(162,plain,
% 0.20/0.50 ($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[161, 160])).
% 0.20/0.50 tff(163,plain,
% 0.20/0.50 ((~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0)) | $greatereq($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(164,plain,
% 0.20/0.50 ($greatereq($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[163, 162])).
% 0.20/0.50 tff(165,plain,
% 0.20/0.50 (^[U: rope1, U1: rope1, U2: $int] : refl(($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0) <=> ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(166,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0) <=> ![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[165])).
% 0.20/0.50 tff(167,plain,
% 0.20/0.50 (^[U: rope1, U1: rope1, U2: $int] : trans(monotonicity(rewrite($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = $sum($product(-1, U2), app_proj_31(app3(U, U1, U2)))), (($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = 0) <=> ($sum($product(-1, U2), app_proj_31(app3(U, U1, U2))) = 0))), rewrite(($sum($product(-1, U2), app_proj_31(app3(U, U1, U2))) = 0) <=> ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)), (($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = 0) <=> ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(168,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : ($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = 0) <=> ![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[167])).
% 0.20/0.50 tff(169,plain,
% 0.20/0.50 (^[U: rope1, U1: rope1, U2: $int] : rewrite((app_proj_31(app3(U, U1, U2)) = U2) <=> ($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = 0))),
% 0.20/0.50 inference(bind,[status(th)],[])).
% 0.20/0.50 tff(170,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : (app_proj_31(app3(U, U1, U2)) = U2) <=> ![U: rope1, U1: rope1, U2: $int] : ($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = 0)),
% 0.20/0.50 inference(quant_intro,[status(thm)],[169])).
% 0.20/0.50 tff(171,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : (app_proj_31(app3(U, U1, U2)) = U2) <=> ![U: rope1, U1: rope1, U2: $int] : (app_proj_31(app3(U, U1, U2)) = U2)),
% 0.20/0.50 inference(rewrite,[status(thm)],[])).
% 0.20/0.50 tff(172,axiom,(![U: rope1, U1: rope1, U2: $int] : (app_proj_31(app3(U, U1, U2)) = U2)), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_proj_3_def1')).
% 0.20/0.50 tff(173,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : (app_proj_31(app3(U, U1, U2)) = U2)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[172, 171])).
% 0.20/0.50 tff(174,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : ($sum(app_proj_31(app3(U, U1, U2)), $product(-1, U2)) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[173, 170])).
% 0.20/0.50 tff(175,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[174, 168])).
% 0.20/0.50 tff(176,plain,(
% 0.20/0.50 ![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)),
% 0.20/0.50 inference(skolemize,[status(sab)],[175])).
% 0.20/0.50 tff(177,plain,
% 0.20/0.50 (![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)),
% 0.20/0.50 inference(modus_ponens,[status(thm)],[176, 166])).
% 0.20/0.50 tff(178,plain,
% 0.20/0.50 ((~![U: rope1, U1: rope1, U2: $int] : ($sum(U2, $product(-1, app_proj_31(app3(U, U1, U2)))) = 0)) | ($sum(X2!7, $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))) = 0)),
% 0.20/0.50 inference(quant_inst,[status(thm)],[])).
% 0.20/0.50 tff(179,plain,
% 0.20/0.50 ($sum(X2!7, $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))) = 0),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[178, 177])).
% 0.20/0.50 tff(180,plain,
% 0.20/0.50 ((~($sum(X2!7, $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))) = 0)) | $lesseq($sum(X2!7, $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(181,plain,
% 0.20/0.50 ($lesseq($sum(X2!7, $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[180, 179])).
% 0.20/0.50 tff(182,plain,
% 0.20/0.50 (app_proj_31(app3(X!9, X1!8, X2!7)) = app_proj_31(R!4)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.50 tff(183,plain,
% 0.20/0.50 (app_proj_31(R!4) = app_proj_31(app3(X!9, X1!8, X2!7))),
% 0.20/0.50 inference(symmetry,[status(thm)],[182])).
% 0.20/0.50 tff(184,plain,
% 0.20/0.50 ((~(app_proj_31(R!4) = app_proj_31(app3(X!9, X1!8, X2!7)))) | $greatereq($sum(app_proj_31(R!4), $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(185,plain,
% 0.20/0.50 ($greatereq($sum(app_proj_31(R!4), $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[184, 183])).
% 0.20/0.50 tff(186,plain,
% 0.20/0.50 (app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8)) = X1!8),
% 0.20/0.50 inference(symmetry,[status(thm)],[73])).
% 0.20/0.50 tff(187,plain,
% 0.20/0.50 (app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))) = X1!8),
% 0.20/0.50 inference(transitivity,[status(thm)],[71, 186])).
% 0.20/0.50 tff(188,plain,
% 0.20/0.50 (length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))) = length4(X1!8)),
% 0.20/0.50 inference(monotonicity,[status(thm)],[187])).
% 0.20/0.50 tff(189,plain,
% 0.20/0.50 (length4(X1!8) = length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8)))))),
% 0.20/0.50 inference(symmetry,[status(thm)],[188])).
% 0.20/0.50 tff(190,plain,
% 0.20/0.50 ((~(length4(X1!8) = length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))) | $greatereq($sum(length4(X1!8), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))), 0)),
% 0.20/0.50 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.50 tff(191,plain,
% 0.20/0.50 ($greatereq($sum(length4(X1!8), $product(-1, length4(app3(app_proj_11(X1!8), app_proj_21(X1!8), tb2t(t2tb(app_proj_31(X1!8))))))), 0)),
% 0.20/0.50 inference(unit_resolution,[status(thm)],[190, 189])).
% 0.20/0.50 tff(192,plain,
% 0.20/0.50 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(app_proj_31(R!4), $product(-1, tb2t(t2tb(app_proj_31(R!4))))) = 0)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(193,plain,
% 0.20/0.51 ($sum(app_proj_31(R!4), $product(-1, tb2t(t2tb(app_proj_31(R!4))))) = 0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[192, 36])).
% 0.20/0.51 tff(194,plain,
% 0.20/0.51 ((~($sum(app_proj_31(R!4), $product(-1, tb2t(t2tb(app_proj_31(R!4))))) = 0)) | $lesseq($sum(app_proj_31(R!4), $product(-1, tb2t(t2tb(app_proj_31(R!4))))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(195,plain,
% 0.20/0.51 ($lesseq($sum(app_proj_31(R!4), $product(-1, tb2t(t2tb(app_proj_31(R!4))))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[194, 193])).
% 0.20/0.51 tff(196,plain,
% 0.20/0.51 (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0)),
% 0.20/0.51 inference(and_elim,[status(thm)],[152])).
% 0.20/0.51 tff(197,plain,
% 0.20/0.51 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(198,plain,
% 0.20/0.51 (sort1(int, t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[197, 7])).
% 0.20/0.51 tff(199,plain,
% 0.20/0.51 (((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | ((~sort1(int, t2tb(app_proj_31(R!4)))) | (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4))))) <=> ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | (~sort1(int, t2tb(app_proj_31(R!4)))) | (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(200,plain,
% 0.20/0.51 ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | ((~sort1(int, t2tb(app_proj_31(R!4)))) | (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4))))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(201,plain,
% 0.20/0.51 ((~![A: ty, Z: uni, Z1: uni, Z2: uni, U: rope1, U1: rope1, U2: $int] : ((~sort1(A, Z2)) | (match_rope1(A, app3(U, U1, U2), Z, Z1, Z2) = Z2))) | (~sort1(int, t2tb(app_proj_31(R!4)))) | (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[200, 199])).
% 0.20/0.51 tff(202,plain,
% 0.20/0.51 ((~sort1(int, t2tb(app_proj_31(R!4)))) | (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[201, 58])).
% 0.20/0.51 tff(203,plain,
% 0.20/0.51 (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4))),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[202, 198])).
% 0.20/0.51 tff(204,plain,
% 0.20/0.51 (match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[154])).
% 0.20/0.51 tff(205,plain,
% 0.20/0.51 (match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = match_rope1(int, app3(X!9, X1!8, X2!7), t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(symmetry,[status(thm)],[204])).
% 0.20/0.51 tff(206,plain,
% 0.20/0.51 (match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))) = t2tb(app_proj_31(R!4))),
% 0.20/0.51 inference(transitivity,[status(thm)],[205, 203])).
% 0.20/0.51 tff(207,plain,
% 0.20/0.51 (tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))) = tb2t(t2tb(app_proj_31(R!4)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[206])).
% 0.20/0.51 tff(208,plain,
% 0.20/0.51 ((~(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))) = tb2t(t2tb(app_proj_31(R!4))))) | $greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $product(-1, tb2t(t2tb(app_proj_31(R!4))))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(209,plain,
% 0.20/0.51 ($greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $product(-1, tb2t(t2tb(app_proj_31(R!4))))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[208, 207])).
% 0.20/0.51 tff(210,plain,
% 0.20/0.51 (inv1(X!9)),
% 0.20/0.51 inference(and_elim,[status(thm)],[152])).
% 0.20/0.51 tff(211,plain,
% 0.20/0.51 (^[R: rope1] : refl(((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0)) <=> ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(212,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0)) <=> ![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[211])).
% 0.20/0.51 tff(213,plain,
% 0.20/0.51 (^[R: rope1] : rewrite(((~inv1(R)) | ($sum(length3(string3(R)), $product(-1, length4(R))) = 0)) <=> ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(214,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | ($sum(length3(string3(R)), $product(-1, length4(R))) = 0)) <=> ![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[213])).
% 0.20/0.51 tff(215,plain,
% 0.20/0.51 (^[R: rope1] : rewrite(((~inv1(R)) | (length3(string3(R)) = length4(R))) <=> ((~inv1(R)) | ($sum(length3(string3(R)), $product(-1, length4(R))) = 0)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(216,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | (length3(string3(R)) = length4(R))) <=> ![R: rope1] : ((~inv1(R)) | ($sum(length3(string3(R)), $product(-1, length4(R))) = 0))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[215])).
% 0.20/0.51 tff(217,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | (length3(string3(R)) = length4(R))) <=> ![R: rope1] : ((~inv1(R)) | (length3(string3(R)) = length4(R)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(218,plain,
% 0.20/0.51 (^[R: rope1] : rewrite((inv1(R) => (length3(string3(R)) = length4(R))) <=> ((~inv1(R)) | (length3(string3(R)) = length4(R))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(219,plain,
% 0.20/0.51 (![R: rope1] : (inv1(R) => (length3(string3(R)) = length4(R))) <=> ![R: rope1] : ((~inv1(R)) | (length3(string3(R)) = length4(R)))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[218])).
% 0.20/0.51 tff(220,axiom,(![R: rope1] : (inv1(R) => (length3(string3(R)) = length4(R)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rope_length_is_string_length')).
% 0.20/0.51 tff(221,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | (length3(string3(R)) = length4(R)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[220, 219])).
% 0.20/0.51 tff(222,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | (length3(string3(R)) = length4(R)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[221, 217])).
% 0.20/0.51 tff(223,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | ($sum(length3(string3(R)), $product(-1, length4(R))) = 0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[222, 216])).
% 0.20/0.51 tff(224,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[223, 214])).
% 0.20/0.51 tff(225,plain,(
% 0.20/0.51 ![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))),
% 0.20/0.51 inference(skolemize,[status(sab)],[224])).
% 0.20/0.51 tff(226,plain,
% 0.20/0.51 (![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[225, 212])).
% 0.20/0.51 tff(227,plain,
% 0.20/0.51 (((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | ((~inv1(X!9)) | ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0))) <=> ((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | (~inv1(X!9)) | ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(228,plain,
% 0.20/0.51 (((~inv1(X!9)) | ($sum(length4(X!9), $product(-1, length3(string3(X!9)))) = 0)) <=> ((~inv1(X!9)) | ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(229,plain,
% 0.20/0.51 (((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | ((~inv1(X!9)) | ($sum(length4(X!9), $product(-1, length3(string3(X!9)))) = 0))) <=> ((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | ((~inv1(X!9)) | ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0)))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[228])).
% 0.20/0.51 tff(230,plain,
% 0.20/0.51 (((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | ((~inv1(X!9)) | ($sum(length4(X!9), $product(-1, length3(string3(X!9)))) = 0))) <=> ((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | (~inv1(X!9)) | ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0))),
% 0.20/0.51 inference(transitivity,[status(thm)],[229, 227])).
% 0.20/0.51 tff(231,plain,
% 0.20/0.51 ((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | ((~inv1(X!9)) | ($sum(length4(X!9), $product(-1, length3(string3(X!9)))) = 0))),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(232,plain,
% 0.20/0.51 ((~![R: rope1] : ((~inv1(R)) | ($sum(length4(R), $product(-1, length3(string3(R)))) = 0))) | (~inv1(X!9)) | ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[231, 230])).
% 0.20/0.51 tff(233,plain,
% 0.20/0.51 ($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[232, 226, 210])).
% 0.20/0.51 tff(234,plain,
% 0.20/0.51 ((~($sum(length3(string3(X!9)), $product(-1, length4(X!9))) = 0)) | $lesseq($sum(length3(string3(X!9)), $product(-1, length4(X!9))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(235,plain,
% 0.20/0.51 ($lesseq($sum(length3(string3(X!9)), $product(-1, length4(X!9))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[234, 233])).
% 0.20/0.51 tff(236,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : refl(($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0) <=> ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(237,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0) <=> ![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[236])).
% 0.20/0.51 tff(238,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : trans(monotonicity(rewrite($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = $sum($product(-1, length3(S2)), $sum(length3(app2(S1, S2)), $product(-1, length3(S1))))), (($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = 0) <=> ($sum($product(-1, length3(S2)), $sum(length3(app2(S1, S2)), $product(-1, length3(S1)))) = 0))), rewrite(($sum($product(-1, length3(S2)), $sum(length3(app2(S1, S2)), $product(-1, length3(S1)))) = 0) <=> ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)), (($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = 0) <=> ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(239,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : ($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = 0) <=> ![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[238])).
% 0.20/0.51 tff(240,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((length3(app2(S1, S2)) = $sum(length3(S1), length3(S2))) <=> ($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = 0))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(241,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (length3(app2(S1, S2)) = $sum(length3(S1), length3(S2))) <=> ![S1: string2, S2: string2] : ($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = 0)),
% 0.20/0.51 inference(quant_intro,[status(thm)],[240])).
% 0.20/0.51 tff(242,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (length3(app2(S1, S2)) = $sum(length3(S1), length3(S2))) <=> ![S1: string2, S2: string2] : (length3(app2(S1, S2)) = $sum(length3(S1), length3(S2)))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(243,axiom,(![S1: string2, S2: string2] : (length3(app2(S1, S2)) = $sum(length3(S1), length3(S2)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','app_def1')).
% 0.20/0.51 tff(244,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (length3(app2(S1, S2)) = $sum(length3(S1), length3(S2)))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[243, 242])).
% 0.20/0.51 tff(245,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : ($sum(length3(app2(S1, S2)), $sum($product(-1, length3(S1)), $product(-1, length3(S2)))) = 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[244, 241])).
% 0.20/0.51 tff(246,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[245, 239])).
% 0.20/0.51 tff(247,plain,(
% 0.20/0.51 ![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)),
% 0.20/0.51 inference(skolemize,[status(sab)],[246])).
% 0.20/0.51 tff(248,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[247, 237])).
% 0.20/0.51 tff(249,plain,
% 0.20/0.51 (((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0)) <=> ((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(250,plain,
% 0.20/0.51 (($sum(length3(string3(X!9)), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))))) = 0) <=> ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0)),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(251,plain,
% 0.20/0.51 (((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string3(X!9)), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))))) = 0)) <=> ((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0))),
% 0.20/0.51 inference(monotonicity,[status(thm)],[250])).
% 0.20/0.51 tff(252,plain,
% 0.20/0.51 (((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string3(X!9)), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))))) = 0)) <=> ((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0))),
% 0.20/0.51 inference(transitivity,[status(thm)],[251, 249])).
% 0.20/0.51 tff(253,plain,
% 0.20/0.51 ((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string3(X!9)), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))))) = 0)),
% 0.20/0.51 inference(quant_inst,[status(thm)],[])).
% 0.20/0.51 tff(254,plain,
% 0.20/0.51 ((~![S1: string2, S2: string2] : ($sum(length3(S2), $sum($product(-1, length3(app2(S1, S2))), length3(S1))) = 0)) | ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0)),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[253, 252])).
% 0.20/0.51 tff(255,plain,
% 0.20/0.51 ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[254, 248])).
% 0.20/0.51 tff(256,plain,
% 0.20/0.51 ((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))) = 0)) | $greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))), 0)),
% 0.20/0.51 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.51 tff(257,plain,
% 0.20/0.51 ($greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))), 0)),
% 0.20/0.51 inference(unit_resolution,[status(thm)],[256, 255])).
% 0.20/0.51 tff(258,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(259,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> ![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[258])).
% 0.20/0.51 tff(260,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : refl((~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(261,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> ![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[260])).
% 0.20/0.51 tff(262,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(263,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> ![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[262])).
% 0.20/0.51 tff(264,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))) <=> ![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))),
% 0.20/0.51 inference(transitivity,[status(thm)],[263, 261])).
% 0.20/0.51 tff(265,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : trans(monotonicity(rewrite(((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> ((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))), trans(monotonicity(rewrite((~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))))) <=> (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))), ((infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1)))))) <=> (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))), rewrite((infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))) <=> (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))), ((infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1)))))) <=> (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))), ((((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))))))) <=> (((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))))), rewrite((((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) <=> (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))), ((((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))))))) <=> (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(266,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))))))) <=> ![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[265])).
% 0.20/0.51 tff(267,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | ((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$greatereq($sum(tptp_fun_I_0(S2, S1), $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1)))))))) <=> (((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(268,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | ((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$greatereq($sum(tptp_fun_I_0(S2, S1), $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1)))))))) <=> ![S1: string2, S2: string2] : (((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1)))))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[267])).
% 0.20/0.51 tff(269,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((infix_eqeq1(S1, S2) <=> (($sum(length3(S1), $product(-1, length3(S2))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(length3(S1), $product(-1, I)), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> (infix_eqeq1(S1, S2) <=> (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(270,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> (($sum(length3(S1), $product(-1, length3(S2))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(length3(S1), $product(-1, I)), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> ![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[269])).
% 0.20/0.51 tff(271,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> (infix_eqeq1(S1, S2) <=> (($sum(length3(S1), $product(-1, length3(S2))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(length3(S1), $product(-1, I)), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(272,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> ![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> (($sum(length3(S1), $product(-1, length3(S2))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(length3(S1), $product(-1, I)), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[271])).
% 0.20/0.51 tff(273,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> ![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(rewrite,[status(thm)],[])).
% 0.20/0.51 tff(274,plain,
% 0.20/0.51 (^[S1: string2, S2: string2] : rewrite((infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : (($lesseq(0, I) & $less(I, length3(S1))) => (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))))),
% 0.20/0.51 inference(bind,[status(th)],[])).
% 0.20/0.51 tff(275,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : (($lesseq(0, I) & $less(I, length3(S1))) => (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) <=> ![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(quant_intro,[status(thm)],[274])).
% 0.20/0.51 tff(276,axiom,(![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : (($lesseq(0, I) & $less(I, length3(S1))) => (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','infix_eqeq_def')).
% 0.20/0.51 tff(277,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[276, 275])).
% 0.20/0.51 tff(278,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> ((length3(S1) = length3(S2)) & ![I: $int] : ((~($lesseq(0, I) & (~$lesseq(length3(S1), I)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[277, 273])).
% 0.20/0.51 tff(279,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> (($sum(length3(S1), $product(-1, length3(S2))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$lesseq($sum(length3(S1), $product(-1, I)), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[278, 272])).
% 0.20/0.51 tff(280,plain,
% 0.20/0.51 (![S1: string2, S2: string2] : (infix_eqeq1(S1, S2) <=> (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)))))),
% 0.20/0.51 inference(modus_ponens,[status(thm)],[279, 270])).
% 0.20/0.51 tff(281,plain,(
% 0.20/0.51 ![S1: string2, S2: string2] : (((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | ((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$greatereq($sum(tptp_fun_I_0(S2, S1), $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))))))))),
% 0.20/0.52 inference(skolemize,[status(sab)],[280])).
% 0.20/0.52 tff(282,plain,
% 0.20/0.52 (![S1: string2, S2: string2] : (((~infix_eqeq1(S1, S2)) | (($sum(length3(S2), $product(-1, length3(S1))) = 0) & ![I: $int] : ((~($greatereq(I, 0) & (~$greatereq($sum(I, $product(-1, length3(S1))), 0)))) | (mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I))))) & (infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((~($greatereq(tptp_fun_I_0(S2, S1), 0) & (~$lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0)))) | (mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1)))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[281, 268])).
% 0.20/0.52 tff(283,plain,
% 0.20/0.52 (![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[282, 266])).
% 0.20/0.52 tff(284,plain,
% 0.20/0.52 (![S1: string2, S2: string2] : (~((~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0))))))) | (~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[283, 264])).
% 0.20/0.52 tff(285,plain,
% 0.20/0.52 (![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))),
% 0.20/0.52 inference(modus_ponens,[status(thm)],[284, 259])).
% 0.20/0.52 tff(286,plain,
% 0.20/0.52 (((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))))) <=> ((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(287,plain,
% 0.20/0.52 ((~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))))) <=> (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))))),
% 0.20/0.52 inference(rewrite,[status(thm)],[])).
% 0.20/0.52 tff(288,plain,
% 0.20/0.52 (((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))))) <=> ((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))))))),
% 0.20/0.52 inference(monotonicity,[status(thm)],[287])).
% 0.20/0.52 tff(289,plain,
% 0.20/0.52 (((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))))) <=> ((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))))))),
% 0.20/0.52 inference(transitivity,[status(thm)],[288, 286])).
% 0.20/0.52 tff(290,plain,
% 0.20/0.52 ((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))))),
% 0.20/0.52 inference(quant_inst,[status(thm)],[])).
% 0.20/0.52 tff(291,plain,
% 0.20/0.52 ((~![S1: string2, S2: string2] : (~((~(infix_eqeq1(S1, S2) | (~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~((mixfix_lbrb1(S1, tptp_fun_I_0(S2, S1)) = mixfix_lbrb1(S2, tptp_fun_I_0(S2, S1))) | $lesseq($sum(length3(S1), $product(-1, tptp_fun_I_0(S2, S1))), 0) | (~$greatereq(tptp_fun_I_0(S2, S1), 0)))))) | (~((~infix_eqeq1(S1, S2)) | (~((~($sum(length3(S2), $product(-1, length3(S1))) = 0)) | (~![I: $int] : ((mixfix_lbrb1(S1, I) = mixfix_lbrb1(S2, I)) | (~$greatereq(I, 0)) | $greatereq($sum(I, $product(-1, length3(S1))), 0)))))))))) | (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[290, 289])).
% 0.20/0.53 tff(292,plain,
% 0.20/0.53 (~((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[291, 285])).
% 0.20/0.53 tff(293,plain,
% 0.20/0.53 (((~(infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))) | (~((mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0) | (~$greatereq(tptp_fun_I_0(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), 0)))) | (~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)))) | (~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))))) | ((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(294,plain,
% 0.20/0.53 ((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[293, 292])).
% 0.20/0.53 tff(295,plain,
% 0.20/0.53 (infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))),
% 0.20/0.53 inference(and_elim,[status(thm)],[152])).
% 0.20/0.53 tff(296,plain,
% 0.20/0.53 ((~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))) | (~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(297,plain,
% 0.20/0.53 ((~((~infix_eqeq1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))))) | (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[296, 295])).
% 0.20/0.53 tff(298,plain,
% 0.20/0.53 (~((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0))))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[297, 294])).
% 0.20/0.53 tff(299,plain,
% 0.20/0.53 (((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | (~![I: $int] : ((~$greatereq(I, 0)) | (mixfix_lbrb1(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))), I) = mixfix_lbrb1(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)), I)) | $greatereq($sum(I, $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))))), 0)))) | ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(300,plain,
% 0.20/0.53 ($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[299, 298])).
% 0.20/0.53 tff(301,plain,
% 0.20/0.53 ((~($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))) = 0)) | $lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(302,plain,
% 0.20/0.53 ($lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[301, 300])).
% 0.20/0.53 tff(303,plain,
% 0.20/0.53 ($lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0)),
% 0.20/0.53 inference(and_elim,[status(thm)],[152])).
% 0.20/0.53 tff(304,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[303, 302, 257, 235, 209, 196, 195, 191, 185, 181, 164, 97, 79])).
% 0.20/0.53 tff(305,plain,(~(X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8)))), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(306,plain,
% 0.20/0.53 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | (tb2t(t2tb(0)) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | (tb2t(t2tb(0)) = 0))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(307,plain,
% 0.20/0.53 (($product(-1, tb2t(t2tb(0))) = 0) <=> (tb2t(t2tb(0)) = 0)),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(308,plain,
% 0.20/0.53 ($sum(0, $product(-1, tb2t(t2tb(0)))) = $product(-1, tb2t(t2tb(0)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(309,plain,
% 0.20/0.53 (($sum(0, $product(-1, tb2t(t2tb(0)))) = 0) <=> ($product(-1, tb2t(t2tb(0))) = 0)),
% 0.20/0.53 inference(monotonicity,[status(thm)],[308])).
% 0.20/0.53 tff(310,plain,
% 0.20/0.53 (($sum(0, $product(-1, tb2t(t2tb(0)))) = 0) <=> (tb2t(t2tb(0)) = 0)),
% 0.20/0.53 inference(transitivity,[status(thm)],[309, 307])).
% 0.20/0.53 tff(311,plain,
% 0.20/0.53 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(0, $product(-1, tb2t(t2tb(0)))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | (tb2t(t2tb(0)) = 0))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[310])).
% 0.20/0.53 tff(312,plain,
% 0.20/0.53 (((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(0, $product(-1, tb2t(t2tb(0)))) = 0)) <=> ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | (tb2t(t2tb(0)) = 0))),
% 0.20/0.53 inference(transitivity,[status(thm)],[311, 306])).
% 0.20/0.53 tff(313,plain,
% 0.20/0.53 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | ($sum(0, $product(-1, tb2t(t2tb(0)))) = 0)),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(314,plain,
% 0.20/0.53 ((~![I: $int] : ($sum(I, $product(-1, tb2t(t2tb(I)))) = 0)) | (tb2t(t2tb(0)) = 0)),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.20/0.53 tff(315,plain,
% 0.20/0.53 (tb2t(t2tb(0)) = 0),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[314, 36])).
% 0.20/0.53 tff(316,plain,
% 0.20/0.53 ((~![X: $int] : sort1(int, t2tb(X))) | sort1(int, t2tb(0))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(317,plain,
% 0.20/0.53 (sort1(int, t2tb(0))),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[316, 7])).
% 0.20/0.53 tff(318,plain,
% 0.20/0.53 (^[A: ty, Z: uni, Z1: uni, Z2: uni] : refl(((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z)) <=> ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(319,plain,
% 0.20/0.53 (![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[318])).
% 0.20/0.53 tff(320,plain,
% 0.20/0.53 (![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(321,plain,
% 0.20/0.53 (^[A: ty, Z: uni, Z1: uni, Z2: uni] : rewrite((sort1(A, Z) => (match_rope1(A, emp1, Z, Z1, Z2) = Z)) <=> ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(322,plain,
% 0.20/0.53 (![A: ty, Z: uni, Z1: uni, Z2: uni] : (sort1(A, Z) => (match_rope1(A, emp1, Z, Z1, Z2) = Z)) <=> ![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[321])).
% 0.20/0.53 tff(323,axiom,(![A: ty, Z: uni, Z1: uni, Z2: uni] : (sort1(A, Z) => (match_rope1(A, emp1, Z, Z1, Z2) = Z))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','match_rope_Emp1')).
% 0.20/0.53 tff(324,plain,
% 0.20/0.53 (![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[323, 322])).
% 0.20/0.53 tff(325,plain,
% 0.20/0.53 (![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[324, 320])).
% 0.20/0.53 tff(326,plain,(
% 0.20/0.53 ![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(skolemize,[status(sab)],[325])).
% 0.20/0.53 tff(327,plain,
% 0.20/0.53 (![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[326, 319])).
% 0.20/0.53 tff(328,plain,
% 0.20/0.53 (((~![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))) | ((~sort1(int, t2tb(0))) | (match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(0)))) <=> ((~![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))) | (~sort1(int, t2tb(0))) | (match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(0)))),
% 0.20/0.53 inference(rewrite,[status(thm)],[])).
% 0.20/0.53 tff(329,plain,
% 0.20/0.53 ((~![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))) | ((~sort1(int, t2tb(0))) | (match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(0)))),
% 0.20/0.53 inference(quant_inst,[status(thm)],[])).
% 0.20/0.53 tff(330,plain,
% 0.20/0.53 ((~![A: ty, Z: uni, Z1: uni, Z2: uni] : ((~sort1(A, Z)) | (match_rope1(A, emp1, Z, Z1, Z2) = Z))) | (~sort1(int, t2tb(0))) | (match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(0))),
% 0.20/0.53 inference(modus_ponens,[status(thm)],[329, 328])).
% 0.20/0.53 tff(331,plain,
% 0.20/0.53 (match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[330, 327, 317])).
% 0.20/0.53 tff(332,assumption,(X1!8 = emp1), introduced(assumption)).
% 0.20/0.53 tff(333,plain,
% 0.20/0.53 (emp1 = X1!8),
% 0.20/0.53 inference(symmetry,[status(thm)],[332])).
% 0.20/0.53 tff(334,plain,
% 0.20/0.53 (match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[333])).
% 0.20/0.53 tff(335,plain,
% 0.20/0.53 (match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = match_rope1(int, emp1, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))),
% 0.20/0.53 inference(symmetry,[status(thm)],[334])).
% 0.20/0.53 tff(336,plain,
% 0.20/0.53 (match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(0)),
% 0.20/0.53 inference(transitivity,[status(thm)],[335, 331])).
% 0.20/0.53 tff(337,plain,
% 0.20/0.53 (tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = tb2t(t2tb(0))),
% 0.20/0.53 inference(monotonicity,[status(thm)],[336])).
% 0.20/0.53 tff(338,plain,
% 0.20/0.53 (tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = 0),
% 0.20/0.53 inference(transitivity,[status(thm)],[337, 315])).
% 0.20/0.53 tff(339,plain,
% 0.20/0.53 (($lesseq(length4(X1!8), 0) | $lesseq(length4(X!9), 0) | (~inv1(X!9)) | (~inv1(X1!8)) | (~($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))) = 0))) | (~$lesseq(length4(X1!8), 0))),
% 0.20/0.53 inference(tautology,[status(thm)],[])).
% 0.20/0.53 tff(340,plain,
% 0.20/0.53 (~$lesseq(length4(X1!8), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[339, 160])).
% 0.20/0.53 tff(341,plain,
% 0.20/0.53 ($greatereq(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), 2) | (~$lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10)))))))), 0)) | (~$lesseq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q2!10))))), $product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9))))), 0)) | (~$greatereq($sum(length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5))))), $sum($product(-1, length3(app2(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))), string3(X!9)))), length3(string3(X!9)))), 0)) | (~$lesseq($sum(length3(string3(X!9)), $product(-1, length4(X!9))), 0)) | (~$greatereq($sum(tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4)))), $product(-1, tb2t(t2tb(app_proj_31(R!4))))), 0)) | $lesseq($sum(fib1($sum(1, max3)), $sum($product(-1, tb2t(match_rope1(int, R!4, t2tb(0), t2tb(str_proj_31(R!4)), t2tb(app_proj_31(R!4))))), $product(-1, length3(string_of_queue1(tb2t1(mk_array1(rope, Q!6, t2tb3(Q1!5)))))))), 0) | (~$lesseq($sum(app_proj_31(R!4), $product(-1, tb2t(t2tb(app_proj_31(R!4))))), 0)) | (~$greatereq($sum(app_proj_31(R!4), $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))), 0)) | (~$lesseq($sum(X2!7, $product(-1, app_proj_31(app3(X!9, X1!8, X2!7)))), 0)) | $lesseq(length4(X1!8), 0) | (~$greatereq($sum(X2!7, $sum($product(-1, length4(X1!8)), $product(-1, length4(X!9)))), 0))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(342,plain,
% 0.20/0.53 ($greatereq(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), 2)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[341, 303, 302, 257, 340, 164, 181, 235, 195, 185, 209, 196])).
% 0.20/0.53 tff(343,plain,
% 0.20/0.53 ((~$lesseq(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), 0)) | (~$greatereq(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), 2))),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(344,plain,
% 0.20/0.53 (~$lesseq(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[343, 342])).
% 0.20/0.53 tff(345,plain,
% 0.20/0.53 ((~(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = 0)) | $lesseq(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), 0)),
% 0.20/0.53 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.53 tff(346,plain,
% 0.20/0.53 (~(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = 0)),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[345, 344])).
% 0.20/0.53 tff(347,plain,
% 0.20/0.53 ($false),
% 0.20/0.53 inference(unit_resolution,[status(thm)],[346, 338])).
% 0.20/0.53 tff(348,plain,(~(X1!8 = emp1)), inference(lemma,lemma(discharge,[]))).
% 0.20/0.53 tff(349,plain,
% 0.20/0.53 (^[U: rope1] : refl(((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1)) <=> ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1)))),
% 0.20/0.53 inference(bind,[status(th)],[])).
% 0.20/0.53 tff(350,plain,
% 0.20/0.53 (![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1)) <=> ![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.53 inference(quant_intro,[status(thm)],[349])).
% 0.20/0.53 tff(351,plain,
% 0.20/0.53 (![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1)) <=> ![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(352,plain,
% 0.20/0.54 (^[U: rope1] : rewrite((((U = emp1) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U)))) | (U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U)))) <=> ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(353,plain,
% 0.20/0.54 (![U: rope1] : (((U = emp1) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U)))) | (U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U)))) <=> ![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.54 inference(quant_intro,[status(thm)],[352])).
% 0.20/0.54 tff(354,axiom,(![U: rope1] : (((U = emp1) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U)))) | (U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))))), file('/export/starexec/sandbox/benchmark/theBenchmark.p','rope_inversion1')).
% 0.20/0.54 tff(355,plain,
% 0.20/0.54 (![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[354, 353])).
% 0.20/0.54 tff(356,plain,
% 0.20/0.54 (![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[355, 351])).
% 0.20/0.54 tff(357,plain,(
% 0.20/0.54 ![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.54 inference(skolemize,[status(sab)],[356])).
% 0.20/0.54 tff(358,plain,
% 0.20/0.54 (![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[357, 350])).
% 0.20/0.54 tff(359,plain,
% 0.20/0.54 (((~![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))) | ((X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))) | (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))) | (X1!8 = emp1))) <=> ((~![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))) | (X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))) | (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))) | (X1!8 = emp1))),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(360,plain,
% 0.20/0.54 ((~![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))) | ((X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))) | (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))) | (X1!8 = emp1))),
% 0.20/0.54 inference(quant_inst,[status(thm)],[])).
% 0.20/0.54 tff(361,plain,
% 0.20/0.54 ((~![U: rope1] : ((U = app3(app_proj_11(U), app_proj_21(U), app_proj_31(U))) | (U = str1(str_proj_11(U), str_proj_21(U), str_proj_31(U))) | (U = emp1))) | (X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))) | (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))) | (X1!8 = emp1)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[360, 359])).
% 0.20/0.54 tff(362,plain,
% 0.20/0.54 ((X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))) | (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))) | (X1!8 = emp1)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[361, 358])).
% 0.20/0.54 tff(363,plain,
% 0.20/0.54 ((X1!8 = app3(app_proj_11(X1!8), app_proj_21(X1!8), app_proj_31(X1!8))) | (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8)))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[362, 348])).
% 0.20/0.54 tff(364,plain,
% 0.20/0.54 (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8))),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[363, 305])).
% 0.20/0.54 tff(365,plain,
% 0.20/0.54 (X1!8 = str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))),
% 0.20/0.54 inference(transitivity,[status(thm)],[364, 46])).
% 0.20/0.54 tff(366,plain,
% 0.20/0.54 (match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = match_rope1(int, str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))), t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[365])).
% 0.20/0.54 tff(367,plain,
% 0.20/0.54 (match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8))) = t2tb(str_proj_31(X1!8))),
% 0.20/0.54 inference(transitivity,[status(thm)],[366, 23])).
% 0.20/0.54 tff(368,plain,
% 0.20/0.54 (tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = tb2t(t2tb(str_proj_31(X1!8)))),
% 0.20/0.54 inference(monotonicity,[status(thm)],[367])).
% 0.20/0.54 tff(369,plain,
% 0.20/0.54 ((~(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))) = tb2t(t2tb(str_proj_31(X1!8))))) | $lesseq($sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))), 0)),
% 0.20/0.54 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.54 tff(370,plain,
% 0.20/0.54 ($lesseq($sum(tb2t(match_rope1(int, X1!8, t2tb(0), t2tb(str_proj_31(X1!8)), t2tb(app_proj_31(X1!8)))), $product(-1, tb2t(t2tb(str_proj_31(X1!8))))), 0)),
% 0.20/0.54 inference(unit_resolution,[status(thm)],[369, 368])).
% 0.20/0.54 tff(371,plain,
% 0.20/0.54 (^[X: string2, X1: $int, X2: $int] : refl(($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0) <=> ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(372,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0) <=> ![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)),
% 0.20/0.54 inference(quant_intro,[status(thm)],[371])).
% 0.20/0.54 tff(373,plain,
% 0.20/0.54 (^[X: string2, X1: $int, X2: $int] : trans(monotonicity(rewrite($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = $sum($product(-1, X2), length4(str1(X, X1, X2)))), (($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = 0) <=> ($sum($product(-1, X2), length4(str1(X, X1, X2))) = 0))), rewrite(($sum($product(-1, X2), length4(str1(X, X1, X2))) = 0) <=> ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)), (($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = 0) <=> ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(374,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : ($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = 0) <=> ![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)),
% 0.20/0.54 inference(quant_intro,[status(thm)],[373])).
% 0.20/0.54 tff(375,plain,
% 0.20/0.54 (^[X: string2, X1: $int, X2: $int] : rewrite((length4(str1(X, X1, X2)) = X2) <=> ($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = 0))),
% 0.20/0.54 inference(bind,[status(th)],[])).
% 0.20/0.54 tff(376,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2) <=> ![X: string2, X1: $int, X2: $int] : ($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = 0)),
% 0.20/0.54 inference(quant_intro,[status(thm)],[375])).
% 0.20/0.54 tff(377,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2) <=> ![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2)),
% 0.20/0.54 inference(rewrite,[status(thm)],[])).
% 0.20/0.54 tff(378,plain,
% 0.20/0.54 ((length4(emp1) = 0) & ![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2)),
% 0.20/0.54 inference(and_elim,[status(thm)],[87])).
% 0.20/0.54 tff(379,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2)),
% 0.20/0.54 inference(and_elim,[status(thm)],[378])).
% 0.20/0.54 tff(380,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : (length4(str1(X, X1, X2)) = X2)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[379, 377])).
% 0.20/0.54 tff(381,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : ($sum(length4(str1(X, X1, X2)), $product(-1, X2)) = 0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[380, 376])).
% 0.20/0.54 tff(382,plain,
% 0.20/0.54 (![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)),
% 0.20/0.54 inference(modus_ponens,[status(thm)],[381, 374])).
% 0.20/0.54 tff(383,plain,(
% 0.20/0.54 ![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)),
% 0.20/0.55 inference(skolemize,[status(sab)],[382])).
% 0.20/0.55 tff(384,plain,
% 0.20/0.55 (![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)),
% 0.20/0.55 inference(modus_ponens,[status(thm)],[383, 372])).
% 0.20/0.55 tff(385,plain,
% 0.20/0.55 ((~![X: string2, X1: $int, X2: $int] : ($sum(X2, $product(-1, length4(str1(X, X1, X2)))) = 0)) | ($sum(tb2t(t2tb(str_proj_31(X1!8))), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))) = 0)),
% 0.20/0.55 inference(quant_inst,[status(thm)],[])).
% 0.20/0.55 tff(386,plain,
% 0.20/0.55 ($sum(tb2t(t2tb(str_proj_31(X1!8))), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))) = 0),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[385, 384])).
% 0.20/0.55 tff(387,plain,
% 0.20/0.55 ((~($sum(tb2t(t2tb(str_proj_31(X1!8))), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))) = 0)) | $lesseq($sum(tb2t(t2tb(str_proj_31(X1!8))), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))), 0)),
% 0.20/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.55 tff(388,plain,
% 0.20/0.55 ($lesseq($sum(tb2t(t2tb(str_proj_31(X1!8))), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))), 0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[387, 386])).
% 0.20/0.55 tff(389,plain,
% 0.20/0.55 (str1(str_proj_11(X1!8), str_proj_21(X1!8), str_proj_31(X1!8)) = X1!8),
% 0.20/0.55 inference(symmetry,[status(thm)],[364])).
% 0.20/0.55 tff(390,plain,
% 0.20/0.55 (str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))) = X1!8),
% 0.20/0.55 inference(transitivity,[status(thm)],[45, 389])).
% 0.20/0.55 tff(391,plain,
% 0.20/0.55 (length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))) = length4(X1!8)),
% 0.20/0.55 inference(monotonicity,[status(thm)],[390])).
% 0.20/0.55 tff(392,plain,
% 0.20/0.55 (length4(X1!8) = length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8)))))),
% 0.20/0.55 inference(symmetry,[status(thm)],[391])).
% 0.20/0.55 tff(393,plain,
% 0.20/0.55 ((~(length4(X1!8) = length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))) | $greatereq($sum(length4(X1!8), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))), 0)),
% 0.20/0.55 inference(theory_lemma,[status(thm)],[])).
% 0.20/0.55 tff(394,plain,
% 0.20/0.55 ($greatereq($sum(length4(X1!8), $product(-1, length4(str1(str_proj_11(X1!8), str_proj_21(X1!8), tb2t(t2tb(str_proj_31(X1!8))))))), 0)),
% 0.20/0.55 inference(unit_resolution,[status(thm)],[393, 392])).
% 0.20/0.55 tff(395,plain,
% 0.20/0.55 ($false),
% 0.20/0.55 inference(theory_lemma,[status(thm)],[303, 302, 257, 235, 209, 196, 195, 394, 185, 181, 164, 388, 370])).
% 0.20/0.55 % SZS output end Proof
%------------------------------------------------------------------------------